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A Justly Neglected Argument Redivivus

What a joy is William A. Williams’s The Evolution of Man Scientifically Disproved (1925)! Previously, I’ve discussed its use of a quotation from “Dr. Traas, a famous paleontologist” who supposedly said that the idea that humans descended from any simian species was “certainly the most foolish ever put forth by a man writing on the history of man”; Traas proved to be Oscar Fraas, with a F instead of a T, and he was writing in 1866. I’ve also discussed its use of a quotation from “W. H. Thompson,” who supposedly said that “The Darwinian theory is now rejected by the majority of biologists, as absurdly inadequate”; Thompson proved to be William Hanna Thomson, with no p, and he was talking about natural selection, not evolution in general, and he was doing so in 1911, fourteen years before Williams’s book was published. But recently I noticed a passage in The Evolution of Man Scientifically Disproved that nicely intertwines two threads of contemporary creationist silliness.

In chapter fourteen, “Chance or Design,” Williams begins a paragraph by saying, “Some one [sic] has counted that Darwin has used phrases of doubt, like ‘We may well suppose,’ 800 times in his two principal books. The whole theory is built up on guesses and suppositions.” As I noted in part 1 of “Who Was the Occupant?” the count appears to derive from “Evolution in the Pulpit,” originally published in the November 22, 1911, issue of the Herald and Presbyter but subsequently republished in The Fundamentals (1910–1915) under the byline “An Occupant of the Pew.” There the claim is that the exact phrase “we may well suppose” appears over eight hundred times, which is clearly wrong—in fact, Darwin seems never to have used the phrase in his own voice in print. Williams wisely hedges by saying “phrases of doubt, like ‘We may well suppose’” (emphasis added), but his retention of the numerical figure suggests that he is ultimately relying on “Evolution in the Pulpit.”

Williams isn’t content to rest there, though. In keeping with the general approach of The Evolution of Man Scientifically Disproved, which is to use pseudomathematics to debunk evolution, he offers a calculation—which, to my delight, is in the a priori spirit of John B. Robinson’s Infidelity Answered by the Father-God and His Family (1875). It will be recalled from “A Justly Neglected Argument” that Robinson estimated that there were about 4370 empirical assertions in On the Origin of Species, used the principle of indifference (also known as the principle of insufficient reason) to assign a probability of 0.5 to each of them, and assumed that the argument of the book was so tightly cumulative as to warrant multiplying the probabilities together. He concluded that the chance of evolution’s being correct was therefore incredibly small—0.54370, which is about 3 ∙ 10-1316—requiring “a blackboard of one hundred and twenty feet in length to write it” (emphasis in original) in full.

Robinson’s argument limped at every turn; it’s to Williams’s credit that he tried to avoid the problems, whether or not he was aware of his predecessor. (He seems not to mention Robinson, or H. L. Hastings, who repeated the argument in his editorial preface to the second edition of Robert Patterson’s The Errors of Evolution, or Patterson.) For, first, he continues, “‘Let us suppose’ that each guess is 95 per cent certain, which is far higher than the average of any.” He is thus giving a lot more credence, if only for the sake of argument, to the empirical assertions in the Origin than Robinson was. “The compound probability would equal .95 raised to the 800th power which would be .000,000,000,000,000,006,281, which means there are 6 chances out of a quintillion that evolution is true.” By my reckoning, 0.95800 is actually about 0.000,000,000,000,000,001,510 (I follow Williams’s convention for commas), i.e., 1.51 ∙ 10-18, so it’s more like 1.5 chances out of a quintillion.

Second, Williams allows, “Since not all of these 800 suppositions are dependent upon [sic: he means “independent of”!] each other, we are willing to multiply this result by 10,000,000,000 which still shows that the theory has less than one chance in a million to be true.” What he says is true, of course, although he is wildly underestimating: it would be 1.5 chances in one hundred million. Here again he’s improving on Robinson, whose argument in effect presupposes implausibly that there is a logical connection—or that Darwin thought there was a logical connection—between the claim that cats with blue eyes are invariably deaf and the claim that pigeons with short beaks have small feet, both appearing on the same page of chapter 1 of the Origin. Williams fails to explain or justify the choice of ten billion as his corrective factor, however, making it hard to evaluate. What if only five of the “suppositions” are mutually independent? Then the probability of evolution’s being true could be 0.955—three chances in four!

Of course, Williams’s argument succumbs to the final problem I posed for Robinson’s argument: it would prove way too much if it were sound. As I wrote in “A Justly Neglected Argument,” “there’s nothing distinctive about the Origin required for the success of the argument: any book containing a large number of assertions of fact advanced in the service of a thesis would be shown to be incredible by the same line of reasoning.” That’s as true of Williams’s argument as it is of Robinson’s argument, despite the small but genuine advantages of the former over the latter. Robinson’s argument was, as I observed, justly neglected. Even though Williams’s demographic arguments were approvingly cited in the creationist literature (e.g., William Bell Riley’s Darwin’s Philosophy and the Flood, a pamphlet from the 1930s) for years, his argument based on Darwin’s “phrases of doubt” seems not to have been. I do not think that the neglect was particularly unjust.